Finite Group Databasebeta

← C2×#10591597 #11863797

Subgroups — C2×#10591597 #11863797

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591597C218yesmaximal, direct product factor
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5239—31nomaximal
10C2×#5187—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#239—24no—
13C2×C3×#239—24no—
14C2×C3×#239—22no—
15C2×C3×#239C2214yes—
16C22×C3×D12—21no—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3—21no—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×#216—24no—
24C2×C3×#216C2214yescomplemented
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3724—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63856—22no—
29#63856C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63662C2214yescomplemented
33#63563C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×C3×#41—31no—
36C22×#239D311yescharacteristic
37C22×C3×Q16—31no—
38C2×#946—31no—
39C22×#216D311yescharacteristic, complemented
40C22×#215—31no—
41C22×#214—31no—
42C2×#924—31no—
43#5239—38no—
44C2×#835—31no—
45C2×#835—31no—
46C2×#835—61no—
47C2×#832—31no—
48C2×#830—31no—
49#5187—38no—
50C2×#821—31no—
51C2×(C2×D3)⋊C8—31no—
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×Q8—22no—
55C2×C32×Q8—21no—
56C2×C32×Q8D414yes—
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C3×#239—216no—
64C3×#239—28no—
65C3×#239—28no—
66C2×C3×D12—28no—
67C2×C3×D12—24no—
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yes—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—28no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3D412yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2312yes—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#216—28no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89#3724—24no—
90(C2×D3)⋊Dic3—24no—
91#3715—28no—
92C2×#452—91noSylow
93C2×C3×#41—34no—
94C2×C3×#41—62no—
95C2×C3×#41—64no—
96C2×C3×#41—64no—
97C22×C3×Q8—21no—
98C22×C3×Q8—31no—
99C22×C3×Q8C2×D311yescharacteristic
100C22×C3×Q8C2×D311yescharacteristic
101C22×C3×D4—31no—
102C22×C3×D4—61no—
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C2×#239—24no—
106C2×#239—24no—
107C2×#239—22no—
108C2×#239C2×D314yes—
109C22×D12—21no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—21no—
112C22×C4×D3C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C2×C3×Q16—34no—
115C2×C3×Q16—64no—
116C22×C3×C8—31no—
117C2×#217—61no—
118#946—34no—
119#946—62no—
120C2×#216—24no—
121C2×#216C2×D314yescomplemented
122C2×#215—34no—
123C2×#215—64no—
124C2×#214—34no—
125C2×#214—64no—
126C2×(C2×D3)⋊C4—61no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130#924—34no—
131#924—62no—
132C2×Dic3⋊C4—61no—
133C2×Dic3⋊C4—61no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—61no—
137C22×C3⋊C8C2×D311yescharacteristic
138#835—34no—
139#835—34no—
140#835—64no—
141#832—34no—
142#830—34no—
143#821—34no—
144(C2×D3)⋊C8—34no—
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—24no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—42no—
152C22×C3×D3—42no—
153C22×C3×D3C2×D412yes—
154C32×Q8—24no—
155C32×Q8—22no—
156C32×Q8C2×D414yes—
157C2×C32×C4—24no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—42no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D412yes—
169C3×D12—216no—
170C3×D12—24no—
171C3×D12—22no—
172C3×D12C2×D414yes—
173C3×C4×D3—216no—
174C3×C4×D3—24no—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×Dic6—22no—
178C3×Dic6—22no—
179C3×Dic6—42no—
180C3⋊(C3⋊C8)—22no—
181C3×C3⋊C8—22no—
182C22×#41—31no—
183C22×Q16—31no—
184C22×SD16—91no—
185C2×C22⋊Q8—91no—
186#452—98no—
187C2×#103—91no—
188C2×#102—91no—
189C2×C22⋊C8—91no—
190C24×C3—31no—
191C24×C3—61no—
192C23×D3—21no—
193C23×D3#6711yescharacteristic
194C3×#41—68no—
195C3×#41—616no—
196C3×#41—68no—
197C2×C3×Q8—22no—
198C2×C3×Q8—21no—
199C2×C3×Q8—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—24no—
202C2×C3×Q8—22no—
203C2×C3×Q8—32no—
204C2×C3×Q8—42no—
205C2×C3×Q8—41no—
206C2×C3×Q8—61no—
207C2×C3×Q8—62no—
208C2×C3×Q8—62no—
209C2×C3×Q8#6714yes—
210C2×C3×Q8#6714yes—
211C2×C3×Q8C22×D312yes—
212C2×C3×Q8C22×D312yes—
213C2×C3×D4—34no—
214C2×C3×D4—32no—
215C2×C3×D4—64no—
216C2×C3×D4—68no—
217C2×C3×D4—61no—
218C2×C3×D4—62no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—41no—
226C22×C3×C4—64no—
227C22×C3×C4—68no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×Dic3—21no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—121no—
237C22×Dic3#6711yescharacteristic
238#239—216no—
239#239—28no—
240#239—28no—
241C2×D12—28no—
242C2×D12—24no—
243C2×D12—22no—
244C2×D12—21no—
245C2×D12#6714yes—
246C2×D12C22×D312yes—
247C2×C4×D3—28no—
248C2×C4×D3—22no—
249C2×C4×D3—22no—
250C2×C4×D3—24no—
251C2×C4×D3#6712yes—
252C2×C4×D3C22×D312yes—
253C2×Dic6—22no—
254C2×Dic6—22no—
255C2×Dic6—21no—
256C2×Dic6C22×D312yes—
257C3×Q16—68no—
258C2×C3×C8—32no—
259C2×C3×C8—62no—
260#217—64no—
261#216—28no—
262#215—68no—
263#214—68no—
264(C2×D3)⋊C4—64no—
265C4⋊Dic3—32no—
266C4⋊Dic3—32no—
267C4⋊Dic3—62no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—121no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273C2×C3⋊C8—22no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280C2×C3⋊C8C22×D312yes—
281C22×C32#12012yes—
282C22×C32#13512yes—
283C22×C32#13712yes—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—22no—
286C2×C3×D3—24no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—48no—
293C32×C4—24no—
294C32×C4#12012yes—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3⋊Dic3—42no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C2×#41—34no—
301C2×#41—62no—
302C2×#41—64no—
303C2×#41—64no—
304C22×Q8—31no—
305C22×Q8D3211yescharacteristic
306C22×D4—31no—
307C22×D4—61no—
308C23×C4—31no—
309C23×C4—61no—
310C2×Q16—34no—
311C2×Q16—64no—
312C2×SD16—94no—
313C2×SD16—184no—
314C22×C8—31no—
315C22×C8—91no—
316C22⋊Q8—94no—
317C22⋊Q8—182no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—181no—
320C2×C22⋊C4—181no—
321#103—94no—
322#102—94no—
323C22⋊C8—94no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—64no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—122no—
332C23×C3—122no—
333C23×C3D3×D411yescharacteristic
334C23×C3C2×#6711yescharacteristic
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—24no—
339C22×D3—22no—
340C22×D3—42no—
341C22×D3—42no—
342C22×D3C2×#6712yes—
343C3×Q8—24no—
344C3×Q8—24no—
345C3×Q8—22no—
346C3×Q8—22no—
347C3×Q8—24no—
348C3×Q8—42no—
349C3×Q8—44no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C3×Q8C2×#6714yes—
354C3×Q8C2×#6714yes—
355C3×D4—34no—
356C3×D4—616no—
357C3×D4—64no—
358C3×D4—62no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—32no—
368C2×C3×C4—42no—
369C2×C3×C4—44no—
370C2×C3×C4—616no—
371C2×C3×C4—62no—
372C2×C3×C4—64no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—122no—
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D412yes—
379C2×C3×C4C2×#6712yes—
380C2×C3×C4C2×#6712yes—
381C2×C3×C4C2×#6711yescharacteristic
382C2×C3×C4C2×#6712yes—
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—42no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3—242no—
394C2×Dic3C2×#6712yes—
395D12—216no—
396D12—24no—
397D12—22no—
398D12C2×#6714yes—
399C4×D3—216no—
400C4×D3—24no—
401C4×D3—22no—
402C4×D3—22no—
403Dic6—22no—
404Dic6—22no—
405Dic6—42no—
406C3×C8—62no—
407C3⋊C8—22no—
408C3⋊C8—62no—
409C3⋊C8—62no—
410C3⋊C8—122no—
411C2×C32#45214yescomplemented
412C2×C32C2×#12011yescharacteristic
413C2×C32C2×#13511yescharacteristic
414C2×C32C2×#13711yescharacteristic
415C3×D3—42no—
416C3×D3—44no—
417C24—31no—
418C24—61no—
419#41—68no—
420#41—616no—
421#41—68no—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8—32no—
425C2×Q8—61no—
426C2×Q8—62no—
427C2×Q8—62no—
428C2×Q8#62514yes—
429C2×Q8C2×D3212yes—
430C2×D4—32no—
431C2×D4—34no—
432C2×D4—64no—
433C2×D4—68no—
434C2×D4—62no—
435C2×D4—61no—
436C22×C4—21no—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—64no—
441C22×C4—68no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—61no—
445C22×C4—181no—
446C22×C4C2×D3211yescharacteristic
447Q16—68no—
448SD16—188no—
449C2×C8—32no—
450C2×C8—62no—
451C2×C8—92no—
452C2×C8—182no—
453C4⋊C4—92no—
454C4⋊C4—184no—
455C4⋊C4—181no—
456C22⋊C4—184no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—64no—
464C22×C3—62no—
465C22×C3—124no—
466C22×C3—128no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3#91812yes—
470C22×C3#91912yes—
471C22×C3#93712yes—
472C22×C3#95012yes—
473C22×C3#95112yes—
474C22×C3#95312yes—
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C22×#6711yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—24no—
481C2×D3—44no—
482C2×D3—48no—
483C2×D3—42no—
484C2×D3—42no—
485C3×C4—24no—
486C3×C4—24no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—44no—
491C3×C4—62no—
492C3×C4—122no—
493C3×C4#93712yes—
494C3×C4#95312yes—
495C3×C4C2×D3×D411yescharacteristic
496C3×C4C22×#6711yescharacteristic
497C3×C4C22×#6711yescharacteristic
498C3×C4C22×#6711yescharacteristic
499Dic3—22no—
500Dic3—42no—
501Dic3—122no—
502Dic3—122no—
503Dic3—242no—
504C32C2×#45211yescharacteristic, complemented, Sylow
505C23—32no—
506C23—62no—
507C23—62no—
508C23—62no—
509C23—64no—
510C23—62no—
511C23—122no—
512C23—122no—
513C23D3×#6711yescharacteristic
514Q8—22no—
515Q8—24no—
516Q8—62no—
517Q8—62no—
518Q8—122no—
519Q8C2×#62514yes—
520D4—34no—
521D4—616no—
522D4—62no—
523D4—64no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—32no—
527C2×C4—616no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—64no—
532C2×C4—62no—
533C2×C4—122no—
534C2×C4—182no—
535C2×C4—362no—
536C2×C4C2×#62512yes—
537C2×C4D3×#6712yes—
538C2×C4D3×#6711yescharacteristic
539C2×C4C22×D3211yescharacteristic
540C8—62no—
541C8—182no—
542C2×C3—21no—
543C2×C3—24no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—122no—
547C2×C3—124no—
548C2×C3#518714yescomplemented
549C2×C3#523914yescomplemented
550C2×C3C2×#91811yescharacteristic
551C2×C3C2×#91911yescharacteristic
552C2×C3C2×#93711yescharacteristic
553C2×C3C2×#95011yescharacteristic
554C2×C3C2×#95111yescharacteristic
555C2×C3C2×#95311yescharacteristic
556D3—42no—
557D3—44no—
558C22—62no—
559C22—64no—
560C22—62no—
561C22—62no—
562C22—122no—
563C22—124no—
564C22—128no—
565C22—122no—
566C22#6394312yes—
567C22#6394912yes—
568C22#6397612yes—
569C22C2×D3×#6711yescharacteristic
570C4—24no—
571C4—62no—
572C4—122no—
573C4—362no—
574C4#6397612yes—
575C4C22×#62511yescharacteristic
576C4C2×D3×#6711yescharacteristic
577C3—21no—
578C3C2×#518711yescharacteristic, complemented
579C3C2×#523911yescharacteristic, complemented
580C2—122no—
581C2—124no—
582C2#1059159714yesdirect product factor
583C2C2×#6394311yescharacteristic
584C2C2×#6394911yescharacteristic
585C2C2×#6397611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×#239C2
hypercenterC22×Q8D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
3. C2×#63856C2semidirect
4. C22×#3715C2semidirect
5. C2×#63662C2semidirect
6. #10591597C2direct (N × H)
7. C2×#63563C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
24. C2×C3×#216C22semidirect
29. #63856C22semidirect
31. C2×#3715C22semidirect
32. #63662C22semidirect
33. #63563C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C22×#216D3semidirect
121. C2×#216C2×D3semidirect
411. C2×C32#452semidirect
504. C32C2×#452semidirect
548. C2×C3#5187semidirect
549. C2×C3#5239semidirect
578. C3C2×#5187semidirect
579. C3C2×#5239semidirect
582. C2#10591597direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#2392
C22×C3×#2162
C2×#638562
C22×#37152
C2×#636622
#105915972
C2×#635632
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52393
C2×#51873